I've got a 'story' Custom Publish Type and 'artist', writer' Taxonomies.

I have to set rewrite rules within the functions.php for that permalinks to appear such as this:

Artist (Taxonomy/Category):
http://www.example.com/isaac-deutscher
(/%artist%)

Author (Taxonomy/Category):
http://www.example.com/jean-paul-sartre
(/%author%)

Story (Custom Publish Type):
http://www.example.com/issac-deutscher/jean-paul-sartre/the-cat-is-under-the-table
(/%artist%/%author%/%story%)

I've attempted some code I discovered in blogs with no success, and should not learn how to solve this.

I am employed in Wordpress 3..1

This may the secret for Story and Artist, although not for Author:

add_action('init', 'custom_init');
add_filter('post_type_link', 'story_permalink', 10, 3);

function custom_init(){  
    $story = array(  
    'query_var' => true,
    'rewrite' => false,
    );
    $artist = array(
    'query_var' => true,
    'rewrite' => true
    );
    $writer = array(
        'query_var' => true,
        'rewrite' => true
    );  

    register_post_type('story', $story);
    register_taxonomy('artist', 'story', $artist);
    register_taxonomy('writer', 'story', $writer);

    global $wp_rewrite;
    $story_structure = '/%artist%/%writer%/%story%';
    $wp_rewrite->add_rewrite_tag("%story%", '([^/]+)', "story=");
    $wp_rewrite->add_permastruct('story', $story_structure, false);
}

function story_permalink($permalink, $post_id, $leavename){
    $post = get_post($post_id);

    $rewritecode = array(
    '%artist%',
    '%writer%',
    $leavename? '' : '%postname%',
    $leavename? '' : '%pagename%',
    );

    if('' != $permalink && !in_array($post->post_status, array('draft', 'pending', 'auto-draft'))){

        if (strpos($permalink, '%artist%') !== FALSE){
        $terms = wp_get_object_terms($post->ID, 'artist');  
        if (!is_wp_error($terms) && !empty($terms) && is_object($terms[0])) $artist = $terms[0]->slug;
        else $artist = 'unassigned-artist';         
        }

    if (strpos($permalink, '%writer%') !== FALSE){
        $terms = wp_get_object_terms($post->ID, 'writer');  
        if (!is_wp_error($terms) && !empty($terms) && is_object($terms[0])) $writer = $terms[0]->slug;
        else $writer = 'unassigned-writer';         
    }           

    $rewritereplace = array(
        $artist,
        $writer,
        $post->post_name,
        $post->post_name,
    );
    $permalink = str_replace($rewritecode, $rewritereplace, $permalink);
    }
    else{
    }
    return $permalink;
}

Hope it will help.